Objective

The use of advanced methods to solve practical and industrially relevant problems by computers has a long history. Whereas Symbolic Computation is concerned with the algorithmic determination of exact solutions to complex mathematical problems, more recent developments in the area of Satisfiability Checking tackle similar problems but with different algorithmic and technological solutions.

Though both communities have made remarkable progress in the last decades, they still need to be strengthened to tackle practical problems of rapidly increasing size and complexity. Their separate tools (computer algebra systems and SMT solvers) are urgently needed to examine prevailing problems with a direct effect to our society. For example, Satisfiability Checking is an essential backend for assuring the security and the safety of computer systems. In various scientific areas, Symbolic Computation enables dealing with large mathematical problems out of reach of pencil and paper developments.

Currently the two communities are largely disjoint and unaware of the achievements of each other, despite strong reasons for them to discuss and collaborate, as they share many central interests. However, researchers from these two communities rarely interact, and also their tools lack common, mutual interfaces for unifiying their strengths. Bridges between the communities in the form of common platforms and roadmaps are necessary to initiate an exchange, and to support and to direct their interaction. These are the main objectives of this CSA. We will initiate a wide range of activities to bring the two communities together, identify common challenges, offer global events and bilateral visits, propose standards, and so on.

We believe that these activities will initiate cross-fertilisation of both fields and bring mutual improvements. Combining the knowledge, experience and the technologies in these communities will enable the development of radically improved software tools

In summary, this proposal was motivated by the following four main problems.

Problem 1 Disjoint communitiesThe two communities of Satisfiability Checking and Symbolic Computation share interests andchallenges, but they are currently not well connected: there are no common communication platforms(journals, conferences etc.), cross-community cooperations are rare, and they do not join their forcesto offer powerful solutions to challenging industrial problems.Problem 2 Missing research roadmapBoth communities would profit from cross-community interactions, however, the potentials arenot clearly identified. Discussions are needed on what the communities can learn from each other,what are the common challenges which they can solve together.Problem 3 Missing standardsThough in Satisfiability Checking the standard input language allows large benchmark sets, benchmarks for non-linear arithmetic theories are still rare, and harder to describe without ambiguity.Problem 4 VisibilityBoth areas are highly relevant in many theoretic as well as practical application domains, however, though their visibility in other areas is increasing, it still does not reflect their importance.

Why is it important for society?Expected Impacts:• European thought-leadership on new and emerging technologies with a strong engagement of scientists, citizens,innovators and policy makers• Improved long-term innovation potential in Europe both from the abundance of novel ideas and the range of actors ready to take them forward• Improved readiness across Europe to engage in silo-breaking research collaboration and to take up new research and innovation practices• Increased take-up of long-term science and technology research results

What are the overall objectives?The overall aim of this project is to create a new research community bridging the gap betweenSatisfiability Checking and Symbolic Computation, whose members will ultimately be wellinformed about both fields, and thus able to combine the knowledge and techniques of bothfields to develop new research and to resolve problems (both academic and industrial) currentlybeyond the scope of either individual field.We call the new community SC2 (SC-square in ASCII, e.g. for the web site), as it will join the communities ofSatisfiability Checking and Symbolic Computation.O1 Build a joint SC2 communityBuild a community of researchers interested in developing technologies at the boundary of the traditionally separate areas of Satisfiability Checking and Symbolic Computation.O2 Create a research roadmapCreate a research roadmap of potentials and challenges, both to the two traditional silos of Satisfiability Checking and Symbolic Computation, but also challenges that only the new joined SC2 communitycan address.O3 Initiate SC2 standardsCreate standards and benchmark libraries such that the SC2 community can share challenges and measure its progress.O4 Increase the visibility of SC2Disseminate research topics and results to other related research areas and to the public, with a specialfocus on young researchers and aiming at gender and geographic balance.